General exact theory of autoresonance in nonautonomous systems

Details General exact theory of autoresonance in nonautonomous systems General exact theory of autoresonance in nonautonomous systems

2003-06-18

arxiv.org/abs/physics/0306139v3

Europhysics Letters, Vol. 70, No 1, pp. 56-62 (2005)

Physics

Accelerator Physics

12 pages, LaTeX; figures added

Scientific paper

A general exact theory of autoresonance (self-sustained resonance) in both dissipative and Hamiltonian nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the aid of a variational principle concerning the power functional. The theory is applied to Duffing oscillators to obtain exact analytical expressions for autoresonance excitations and solutions which explain all the phenomenological and approximate results arising from the previous approach to autoresonance phenomena.

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